Entropic Effects in Solvent-Free Bidisperse Polymer Brushes Investigated Using Density Functional Theories

Abstract

Solvent-free polymer-functionalized nanoparticles form a special type of colloid composed of inorganic cores self-suspended by their grafted coronas. In the absence of intervening solvent molecules, the fluidity of the system is provided by these tethered polymers as they fill the space.Here, we study the structure and interaction of neighboring polymer-grafted surfaces in the solvent-free condition using mean-field density functional theories. For opposing flat surfaces, the brush configuration and the associated energy landscape are semianalytically investigated given the incompressibility of the tethered entropic chains. The effect of brush polydispersity (including variations in both chain length and surface grafting density) is considered by two bidisperse models corresponding to different physical scenarios: one for opposing brushes uniformly mixed with two species at a fixed grafting density, and the other for opposing brushes with distinct chain lengths and grafting densities. The space-filling capabilities of the neighboring coronas differ not only by their ratio of radii of gyration for the composing polymers but also by their ratio of grafting densities. We show that the system energy depicts a steric repulsion as the brushes are compressed, which is typical for hairy particles in a solvent. However, as the interwall separation increases, the cooperative stretching of the chains leads to an entropic attraction between them, a unique characteristic of solventless systems. The corresponding brush profiles change from a bell-like shape to a more step-function-like feature as the interwall spacing increases significantly. The interwall separation associated with the overall free energy minimum therefore characterizes the favorable interparticle spacing for solvent-free polymer-functionalized particles. The limiting accessible parameter space of polymer sizes and grafting densities subjected to the space-filling constraint is comprehensively explored for representative interparticle spacing characterizing the compressed, relaxed, and stretched regimes for a given polymer species, respectively. Such information would be useful for guiding the design of experimental solvent-free polymerfunctionalized nanoparticles.

Structural and Dynamical Coupling in Solvent-Free Polymer Brushes Elucidated by Molecular Dynamics Simulations

“…Consequently, the collaborative behavior of the two polymers is observed and the longer polymers 1 are more capable to fill the middle region of the gap, while the shorter polymers 2 are more localized to the grafting bottom wall. Such a feature has been qualitatively predicted in the previous DFT study 64 and is unique to bidisperse interacting brushes in the solvent-free condition. In Figure 8a, as the gap thickness increases, the extent of mixing of the opposing brushes gradually decreases and the entropy components slightly reduce accordingly.…”

“…We have demonstrated that the general structural features observed are consistent with the previous DFT predictions. 64 The analyzed segmental relaxations not only qualitatively agree with relevant experimental measurements 57,65,66 but also provide a solid connection with the associated chain configuration.…”

Interactions between Sterically Stabilized Nanoparticles: The Effects of Brush Bidispersity and Chain Stiffness

“…An appealing alternative is provided by mean-field techniques, such as self-consistent field theory [ 10 , 29 , 30 ], integral equation theory [ 31 , 32 , 33 , 34 ], and density functional theory (DFT) [ 9 , 12 , 35 ]. The latter method has been already applied to study solvent-free polymer brushes [ 36 ]. However, to the best of our knowledge, the existing studies of solvent-free brush systems are limited to fully flexible grafted chains.…”

Dynamics of Opposing Polymer Brushes: A Computer Simulation Study

“…Opposing polymer brushes, i.e., systems consisting of two parallel surfaces, both grafted with chains, were also a subject of considerable interest [36]. Theoretical treatment concerned mainly the compression of such brushes [37][38][39][40][41]. Computer simulations were found to be a useful tool for studying opposing polymer brushes-structure, interaction, and friction between a pair of brushes (neutral and charged) were recently investigated [39,[42][43][44][45][46][47][48].…”